The electrochemical behavior of a system with a limited number of molecules

In this paper, based on Einstein relationship between diffusion and random walk, the electrochemical behavior of a system with a limited number of molecules was simulated and explored theoretically. The transition of the current vs time responses from discrete to continuous was clearly obtained as the number of redox molecules increased from 10 to 10(6).

Investigation of Chemical Bond Characteristics, Thermal Expansion Coefficients and Bulk Moduli of alpha-R2MoO6 and R2Mo2O7 (R = rare earths) by Using a Dielectric Chemical Bond Method

Theoretical researches are performed on the alpha-R2MoO6 (R = Y, Gd, Tb Dy, Ho, Er, Tm and Yb) and pyrochlore-type R2Mo2O7 (R = Y, Nd, Sm, Gd, Tb and Dy) rare earth molybdates by using chemical bond theory of dielectric description. The chemical bonding characteristics and their relationship with thermal expansion property and compressibility are explored. The calculated values of linear thermal expansion coefficient (LTEC) and bulk modulus agree well with the available experimental values. The calculations reveal that the LTECs and the bulk moduli do have linear relationship with the ionic radii of the lanthanides: the LTEC decreases from 6.80 to 6.62 10(-6)/K and the bulk modulus increases from 141 to 154 GPa when R goes in the order Gd, Tb Dy, Ho, Er, Tm, and Yb in the alpha-R2MoO6 series; while in the R2Mo2O7 series, the LTEC ranges from 6.80 to 6.61 10(-6)/K and the bulk modulus ranges from 147 to 163 GPa when R varies in the order Nd, Sm, Gd, Tb and Dy.

Calculation of the bulk modulus of simple and complex crystals with the chemical bond method

The relation between the lattice energies and the bulk moduli on binary inorganic crystals was studied, and the concept of lattice energy density is introduced. We find that the lattice energy densities are in good linear relation with the bulk moduli in the same type of crystals, the slopes of fitting lines for various types of crystals are related to the valence and coordination number of cations of crystals, and the empirical expression of calculated slope is obtained. From crystal structure, the calculated results are in very good agreement with the experimental values. At the same time, by means of the dielectric theory of the chemical bond and the calculating method of the lattice energy of complex crystals, the estimative method of the bulk modulus of complex crystals was established reasonably, and the calculated results are in very good agreement with the experimental values.

What has brought on the effects of number-average molecular weight on the spinodals in polymer mixtures?

On the basis of the thermodynamics of Gibbs, the spinodal for the quasibinary system was derived in the framework of the Sanchez-Lacombe lattice fluid theory. All of the spinodals were calculated based on a model polydisperse polymer mixture, where each polymer contains three different molecular weight subcomponents. According to our calculations, the spinodal depends on both weight-average ((M) over bar (w)) and number-average ((M) over bar (n)) molecular weights, whereas that of the z-average molecular weight is invisible. Moreover, the extreme of the spinodal decreases when the polydispersity index (eta = (M) over bar (w)/(M) over bar (n)) of the polymer increases. The effect of polydispersity on the spinodal decreases when the molecular weight gets larger and can be negligible at a certain large molecular weight. It is well-known that the influence of polydispersity on the phase equilibrium (coexisting curve, cloud point curves) is much more pronounced than on the spinodal. The effect of M, on the spinodal is discussed as it results from the infuluence of composition temperatures, molecular weight, and the latter's distribution on free volume. An approximate expression, which is in the assumptions of v* v(1)* = v(2)* and 1/r --> 0 for both of the polymers, was also derived for simplification. It can be used in high molecular weight, although it failed to make visible the effect of number-average molecular weight on the spinodal.

A novel electrochemical method for simultaneously measuring diffusion coefficient and ion transference number

This paper introduces a new method to estimate the diffusion coefficient and transference number of a salt or an electroactive ion in a solution with little or no supporting electrolyte. The above two parameters can be obtained from a single potential step experiment without previous knowledge of either one. It would appear that the method could also be used in the study of ion transport in a high viscosity solvent or a solid electrolyte. (C) 1998 Elsevier Science S.A.

Outer wave number spectrum and statistical distribution of apparent wave number vector

Based on the ray theory and Longuet-Higgins's linear,model of sea waves, the joint distribution of wave envelope and apparent wave number vector is established. From the joint distribution, we define a new concept, namely the outer wave number spectrum, to describe the outer characteristics of ocean waves. The analytical form of the outer wave number spectrum, the probability distributions of the apparent wave number vector and its components are then derived. The outer wave number spectrum is compared with the inner wave number spectrum for the average status of wind-wave development corresponding to a peakness factor P = 3. Discussions on the similarity and difference between the outer wave number spectrum and inner one are also presented in the paper. (C) 2002 Elsevier Science Ltd. All rights reserved.

二氧化碳在孔隙咸水层中多相流动数值模拟研究

There has been a growing concern about the use of fossil fuels and its adverse effects on the atmospheric greenhouse and ecological environment. A reduction in the release rate of CO2 into the atmosphere poses a major challenge to the land ecology of China. The most promising way of achieving CO2 reduction is to dispose of CO2 in deep saline aquifers. Deep aquifers have a large potential for CO2 sequestration in geological medium in terms of volume and duration. Through the numerical simulation of multiphase flow in a porous media, the transformation and motion of CO2 in saline aquifers has been implemented under various temperature and hydrostatic pressure conditions, which plays an important role to the assessment of the reliability and safety of CO2 geological storage. As expected, the calculated results can provide meaningful and scientific information for management purposes. The key problem to the numerical simulation of multiphase flow in a porous media is to accurately capture the mass interface and to deal with the geological heterogeneity. In this study, the updated CE/SE (Space and time conservation element and solution element) method has been proposed, and the Hybrid Particle Level Set method (HPLS) has extended for multiphase flows in porous medium, which can accurately trace the transformation of the mass interface. The benchmark problems have been applied to evaluate and validate the proposed method. In this study, the reliability of CO2 storage in saline aquifers in Daqingzi oil field in Sunlong basin has been discussed. The simulation code developed in this study takes into account the state for CO2 covering the triple point temperature and pressure to the supercritical region. The geological heterogeneity has been implemented, using the well known geostatistical model (GSLIB) on the base of the hard data. The 2D and 3D model have been set up to simulate the CO2 multiphase flow in the porous saline aquifer, applying the CE/SE method and the HPLS method .The main contents and results are summarized as followings. (1) The 2D CE/SE method with first and second –order accuracy has been extended to simulate the multiphase flow in porous medium, which takes into account the contribution of source and sink in the momentum equation. The 3D CE/SE method with the first accuracy has been deduced. The accuracy and efficiency of the proposed CE/SE method have been investigated, using the benchmark problems. (2) The hybrid particle level set method has been made appropriate and extended for capturing the mass interface of multiphase flows in porous media, and the numerical method for level set function calculated has been formulated. (3) The closed equations for multiphase flow in porous medium has been developed, adept to both the Darcy flow and non-Darcy flow, getting over the limitation of Reynolds number to the calculation. It is found that Darcy number has a decisive influence on pressure as well as velocity given the Darcy number. (4) The new Euler scheme for numerical simulations of multiphase flows in porous medium has been proposed, which is efficient and can accurately capture the mass interface. The artificial compressibility method has been used to couple the velocities and pressure. It is found that the Darcy number has determinant effects on the numerical convergence and stability. In terms of the different Darcy numbers, the coefficient of artificial compressibility and the time step have been obtained. (5) The time scale of the critical instability for critical CO2 in the saline aquifer has been found, which is comparable with that of completely CO2 dissolved saline aquifer. (6) The concept model for CO2 multiphase flows in the saline aquifer has been configured, based on the temperature, pressure, porosity as well as permeability of the field site .Numerical simulation of CO2 hydrodynamic trapping in saline aquifers has been performed, applying the proposed CE/SE method. The state for CO2 has been employed to take into account realistic reservoir conditions for CO2 geological sequestration. The geological heterogeneity has been sufficiently treated , using the geostatistical model. (7) It is found that the Rayleigh-Taylor instability phenomenon, which is associated with the penetration of saline fluid into CO2 fluid in the direction of gravity, has been observed in CO2 multiphase flows in the saline aquifer. Development of a mushroom-type spike is a strong indication of the formation of Kelvin-Helmholtz instability due to the developed short wavelength perturbations present along the interface and parallel to the bulk flow. Additional key findings: the geological heterogeneity can distort the flow convection. The ascending of CO2 can induce the persistent flow cycling effects. The results show that boundary conditions of the field site have determinant effects on the transformation and motion of CO2 in saline aquifers. It is confirmed that the proposed method and numerical model has the reliability to simulate the process of the hydrodynamic trapping, which is the controlling mechanism for the initial period of CO2 storage at time scale of 100 years.

地震波场模拟及叠前深度偏移的李群方法

The processes of seismic wave propagation in phase space and one way wave extrapolation in frequency-space domain, if without dissipation, are essentially transformation under the action of one parameter Lie groups. Consequently, the numerical calculation methods of the propagation ought to be Lie group transformation too, which is known as Lie group method. After a fruitful study on the fast methods in matrix inversion, some of the Lie group methods in seismic numerical modeling and depth migration are presented here. Firstly the Lie group description and method of seismic wave propagation in phase space is proposed, which is, in other words, symplectic group description and method for seismic wave propagation, since symplectic group is a Lie subgroup and symplectic method is a special Lie group method. Under the frame of Hamiltonian, the propagation of seismic wave is a symplectic group transformation with one parameter and consequently, the numerical calculation methods of the propagation ought to be symplectic method. After discrete the wave field in time and phase space, many explicit, implicit and leap-frog symplectic schemes are deduced for numerical modeling. Compared to symplectic schemes, Finite difference (FD) method is an approximate of symplectic method. Consequently, explicit, implicit and leap-frog symplectic schemes and FD method are applied in the same conditions to get a wave field in constant velocity model, a synthetic model and Marmousi model. The result illustrates the potential power of the symplectic methods. As an application, symplectic method is employed to give synthetic seismic record of Qinghai foothills model. Another application is the development of Ray+symplectic reverse-time migration method. To make a reasonable balance between the computational efficiency and accuracy, we combine the multi-valued wave field & Green function algorithm with symplectic reverse time migration and thus develop a new ray+wave equation prestack depth migration method. Marmousi model data and Qinghai foothills model data are processed here. The result shows that our method is a better alternative to ray migration for complex structure imaging. Similarly, the extrapolation of one way wave in frequency-space domain is a Lie group transformation with one parameter Z and consequently, the numerical calculation methods of the extrapolation ought to be Lie group methods. After discrete the wave field in depth and space, the Lie group transformation has the form of matrix exponential and each approximation of it gives a Lie group algorithm. Though Pade symmetrical series approximation of matrix exponential gives a extrapolation method which is traditionally regarded as implicit FD migration, it benefits the theoretic and applying study of seismic imaging for it represent the depth extrapolation and migration method in a entirely different way. While, the technique of coordinates of second kind for the approximation of the matrix exponential begins a new way to develop migration operator. The inversion of matrix plays a vital role in the numerical migration method given by Pade symmetrical series approximation. The matrix has a Toepelitz structure with a helical boundary condition and is easy to inverse with LU decomposition. A efficient LU decomposition method is spectral factorization. That is, after the minimum phase correlative function of each array of matrix had be given by a spectral factorization method, all of the functions are arranged in a position according to its former location to get a lower triangular matrix. The major merit of LU decomposition with spectral factorization (SF Decomposition) is its efficiency in dealing with a large number of matrixes. After the setup of a table of the spectral factorization results of each array of matrix, the SF decomposition can give the lower triangular matrix by reading the table. However, the relationship among arrays is ignored in this method, which brings errors in decomposition method. Especially for numerical calculation in complex model, the errors is fatal. Direct elimination method can give the exact LU decomposition But even it is simplified in our case, the large number of decomposition cost unendurable computer time. A hybrid method is proposed here, which combines spectral factorization with direct elimination. Its decomposition errors is 10 times little than that of spectral factorization, and its decomposition speed is quite faster than that of direct elimination, especially in dealing with a large number of matrix. With the hybrid method, the 3D implicit migration can be expected to apply on real seismic data. Finally, the impulse response of 3D implicit migration operator is presented.

Effect of pore ring number of zeolites on catalytic performance of Mo/Zeolite in methane aromatization under non-oxygen condition

The catalytic behavior of Mo-based zeolite catalysts with different pore structure and size, particularly with 8 membered ring ( M R), 10 M R, coexisted 10 and 12 M R, and 12 M R, was studied in methane aromatization under the conditions of SV=1500 ml/(g.h), p=0.1 MPa and T = 973 K. It was found that the catalytic performance is correlated with the pore structure of the zeolite supports. The zeolites that possess 10 MR or 10 and 12 MR pore structure with a pore diameter equal to or slightly larger than the dynamic diameter of benzene molecule, such as ZSM-5, ZSM-11, ZRP-1 and MCM-22, are fine supports. Among the tested zeolite supports, MCM-22 exhibits the highest activity and selectivity for benzene. A methane conversion of 10.5% with benzene selectivity of 80% was achieved over Mo/MCM-22 catalyst. The Mo/ERS-7 catalyst with 8 MR (0.45 nm) does not show any activity in methane dehydro-aromatization, while Mo/JQX-1 and Mo/SBA-15 catalysts with 12 MR pore exhibit little activity in the reaction. It can be concluded that the zeolites with 10 MR pore or coexisted 10 and 12 MR, having pore size equal to or slightly larger than the dynamic diameter of benzene molecule, are fine supports for methane activation and aromatization.

Automatically Recovering Geometry and Texture from Large Sets of Calibrated Images

Three-dimensional models which contain both geometry and texture have numerous applications such as urban planning, physical simulation, and virtual environments. A major focus of computer vision (and recently graphics) research is the automatic recovery of three-dimensional models from two-dimensional images. After many years of research this goal is yet to be achieved. Most practical modeling systems require substantial human input and unlike automatic systems are not scalable. This thesis presents a novel method for automatically recovering dense surface patches using large sets (1000's) of calibrated images taken from arbitrary positions within the scene. Physical instruments, such as Global Positioning System (GPS), inertial sensors, and inclinometers, are used to estimate the position and orientation of each image. Essentially, the problem is to find corresponding points in each of the images. Once a correspondence has been established, calculating its three-dimensional position is simply a matter of geometry. Long baseline images improve the accuracy. Short baseline images and the large number of images greatly simplifies the correspondence problem. The initial stage of the algorithm is completely local and scales linearly with the number of images. Subsequent stages are global in nature, exploit geometric constraints, and scale quadratically with the complexity of the underlying scene. We describe techniques for: 1) detecting and localizing surface patches; 2) refining camera calibration estimates and rejecting false positive surfels; and 3) grouping surface patches into surfaces and growing the surface along a two-dimensional manifold. We also discuss a method for producing high quality, textured three-dimensional models from these surfaces. Some of the most important characteristics of this approach are that it: 1) uses and refines noisy calibration estimates; 2) compensates for large variations in illumination; 3) tolerates significant soft occlusion (e.g. tree branches); and 4) associates, at a fundamental level, an estimated normal (i.e. no frontal-planar assumption) and texture with each surface patch.